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The advent of single-cell RNA sequencing (scRNA-seq) technology enables researchers to gain deep insights into cellular heterogeneity. However, the high dimensionality and noise of scRNA-seq data pose significant challenges to clustering. Therefore, we propose a new single-cell type identification method, called CHLSPCA, to address these challenges. In this model, we innovatively combine correntropy with PCA to address the noise and outliers inherent in scRNA-seq data. Meanwhile, we integrate the hypergraph into the model to extract more valuable information from the local structure of the original data. Subsequently, to capture crucial similarity information not considered by the PCA model, we employ the Gaussian kernel function and the Euclidean metric to mine the similarity information between cells, and incorporate this information into the model as the similarity constraint. Furthermore, the principal components (PCs) of PCA are very dense. A new sparse constraint is introduced into the model to gain sparse PCs. Finally, based on the principal direction matrix learned from CHLSPCA, we conduct extensive downstream analyses on real scRNA-seq datasets. The experimental results show that CHLSPCA performs better than many popular clustering methods and is expected to promote the understanding of cellular heterogeneity in scRNA-seq data analysis and support biomedical research. [ABSTRACT FROM AUTHOR]

Least-squares reverse-time migration (LSRTM) has become an advanced technique for complex structures imaging of the subsurface, as it can provide a higher resolution and more balanced amplitude migrated image than conventional reverse-time migration (RTM). However, the intrinsic attenuation of the subsurface introduces amplitude attenuation and phase dispersion of the seismic wavefield, which leads to an inexact inverted image kinematically and dynamically. Moreover, the imperfect geometry, limited bandwidth of seismic data, and inappropriate modeling kernel etc. would inevitably introduce two side-effects in the migrated image, resulting in degradation of LSRTM imaging potential. To alleviate these issues, we present a data-domain sparsity constraint viscoacoustic LSRTM algorithm in this paper. In particular, we use the decoupled constant Q fractional Laplacian viscoacoustic wave equation as the modeling kernel to describe the attenuation effects of the subsurface, while a model constraint constructed in the misfit function via the L1-2 norm is carried out to clear the migrated artifacts and boost the imaging resolution. Thanks to the excellent performance in sparsity, the drawbacks of unconstrained LSRTM can be effectively mitigated by the L1-2 norm-based regularization. In this paper, we adopt the alternating direction of multipliers method to iteratively address the constrained L1-2 minimization problem by implementing a proximal operator, and three synthetic examples are used to evaluate the effectiveness and practicability of the proposed strategy. Migration results prove that the proposed scheme can effectively compensate for the attenuation effects, improve the resolution, and suppress the migration artifacts of inverted images even in the complex imaging situations. [ABSTRACT FROM AUTHOR]

Hyperspectral unmixing is a key technology in the development of remote sensing applications. However, since both endmembers and abundances are unknown, unmixing is a non-convex problem with a large solution space. To solve this, existing methods usually impose the same strength of sparsity constraint. However, this often does not hold in practice. Because the abundances of purer regions are generally sparse, while the abundances distribution of more mixed regions should be smoother. Temperature scaling is a technique of introducing a temperature parameter T into softmax activation function to adjust the sparsity of the output. Inspired by this, we propose a temperature scaling unmixing (TSU) framework based on convolutional autoencoder (CAE). In this framework, sparse constraints of different intensities are applied to diverse regions by considering spatial similarity of ground objects distribution while preserving the ability of CAE to extract spatial features. What is more, equal-frequency binning is adopted to guide the division of regions by similarity matrix to realize the automatic temperature parameter setting. In addition, a CAE network is designed under the TSU framework in this paper, called TSUCAE. The TSUCAE method exhibits superior accuracy compared to state-of-the-art approaches, as demonstrated through extensive comparative experiments. Furthermore, the TSU framework can be transferred to other CAE-based unmixing methods directly while keeping the network structure of these methods unchanged. Sufficient ablation experiments also prove that the transfer of framework can improve the performance of unmixing. The code is publicly available at https://github.com/UPCGIT/TSUCAE.

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Magnetic resonance (MR) imaging is considered as a very powerful imaging modality in clinical examination, but the process of image acquisition and transmission will be affected by noise, resulting in the degradation of imaging quality. In this paper, based on the Laplacian prior sparsity constraint and the nonconvex second order total variation (TV) penalty, we propose a MR images denoising model which consists of three terms. Specifically, in the first term, we use the L2-norm as the fidelity term to control the proximity between the observed image and the recovered MR image. Then, we introduce the Laplacian sparse prior constraint as the second term to mitigate the staircase artifacts in the recovered image. In the third term, we adopt the nonconvex second-order TV penalty to preserve important textures and edges. Finally, we use the alternating direction method of multipliers to solve the corresponding minimization problem. Comparative experiments on clinical data demonstrate the effectiveness of our approach in terms of PSNR and SSIM values.

We consider the class of mathematical programs with orthogonality type constraints. Orthogonality type constraints appear by reformulating the sparsity constraint via auxiliary binary variables and relaxing them afterwards. For mathematical programs with orthogonality type constraints a necessary optimality condition in terms of T-stationarity is stated. The justification of T-stationarity is threefold. First, it allows to capture the global structure of mathematical programs with orthogonality type constraints in terms of Morse theory, i. e. deformation and cell-attachment results are established. For that, nondegeneracy for the T-stationary points is introduced and shown to hold generically. Second, we prove that Karush-Kuhn-Tucker points of the Scholtes-type regularization converge to T-stationary points of mathematical programs with orthogonality type constraints. This is done under the tailored linear independence constraint qualification, which turns out to be a generic property too. Third, we show that T-stationarity applied to the relaxation of sparsity constrained nonlinear optimization naturally leads to its M-stationary points. Moreover, we argue that all T-stationary points of this relaxation become degenerate. [ABSTRACT FROM AUTHOR]

The traditional nonnegative matrix factorization methods are based on single-layer model. The deep nonnegative matrix factorization methods are based on the mathematical theory, ignoring the actual spectral mixing process of materials. This paper started from the physical process of spectral mixing, combining the advantages of traditional nonnegative matrix factorization models and deep learning. Aiming at the problem that the deep nonnegative matrix factorization methods ignore the actual spectral mixing process of materials, the spectral mixing process is reversed from the physical spectral mixing process. Furthermore, considering the sparsity and spatial smoothness of the distribution of the endmembers in the two-dimensional space, the total variation and sparsity regularized deep nonnegative matrix factorization based on the endmember matrix is proposed. This paper verified the effectiveness of the proposed method through synthetic experiments and real data experiments, which is compared with five classical hyperspectral unmixing methods. Compared with SDNMF-TV, SAD and RMSE are reduced. The results both in the synthetic experiments and the real experiments shows that the method in this paper achieves the best unmixing results. [ABSTRACT FROM AUTHOR]

Kernel adaptive filtering algorithms have been successfully applied in many areas, among which the fraction lower power order statistics error criterion (FLP) is a better choice due to its prominent performance in robust design. However, the growth of network size in kernel adaptive filtering affects the convergence rate and testing accuracy. This paper proposes a sparse Gaussian kernel adaptive filtering algorithm based on the Softplus function framework to address the network size. The framework is constituted by the fraction lower power order statistics error criterion and an improved novelty criterion. The exponential loss function is employed to describe a new novel criterion, which can accurately achieve fast classification and limit the data selection of the dictionary size. This new algorithm is called the kernel fraction lower power order statistics error criterion based on the Softplus function with a modified novelty criterion (SKFLP-MNC) algorithm. In particular, the proposed method is employed for the Mackey–Glass chaotic time series prediction and noise cancellation under the cases of Gaussian and non-Gaussian noise. Simulation results show that the filtering accuracy of the SKFLP-MNC algorithm, the dictionary size, and steady-state mean-squared errors rival some of the sparse kernel least mean square algorithms. [ABSTRACT FROM AUTHOR]

Inversion of gravity data is one the important steps in the interpretation of practical data. The detection of sharp boundaries between anomalous bodies and host rocks is an interesting point in the geological frameworks. The gravity inversion with sparsity constraint is a useful method to recover block subsurface density distribution, which is efficiently used for the quantitative interpretation of gravity data. The reweighted regularized method is a useful method to solve the inverse problem. However, in this type, we must face the updating gravity forward matrix and large matrix operation. The application of Lanczos bidiagonalization method can reduce the size of data and matrix in the inversion to resolve the large scale inversion problem. However, a very important problem is not resolved, which is update of reweighted forward matrix and new Lanczos bidiagonalization matrix. Here, an adaptive Lanczos bidiagonalization method is studied to select the Lanczos bidiagonalization factor. And a new projected method with adaptive Lanczos bidiagonalization method is study to avoid the updating sparsity reweighted function. We calculate the reweighted forward matrix and Lanczos bidiagonalization matrix only one time, which can essentially reduce the computational complexity. The inversion results of synthetic data show that the new improved method is faster and better than common reweight regularized Lanczos bidiagonalization method to produce an acceptable solution for focusing inverse problem. The improvement of adaptive Lanczos bidiagonalization in sparsity gravity inversion is also tested on gravity data collected over the Mobrun massive sulfide ore body in Noranda, Quebec, Canada. The inversion results indicate a remarkable correlation with true structure of the ore body that is achieved from drilling data.

In this paper, a multiple-image authentication method is proposed based on metasurface and phase retrieval with sparsity constraints. In the encryption process, multiple plaintext images are firstly encrypted to a phase-only hologram by using phase retrieval algorithm with sparsity constraints and iterative Fourier transform algorithm, and then the phase-only hologram is converted into a metasurface hologram for multiple-image authentication with the help of a geometric-phase metasurface unit, greatly expanding the encoding information capacity of metasurface for authentication. In the authentication process, the reconstructed image of metasurface hologram is respectively authenticated with multiple plaintext images through nonlinear correlation authentication such that multiple identities of the user holding this metasurface can be simultaneously verified, overcoming the problem that the metasurface for authentication and user identity can only be one-to-one, and substantially improving the efficiency of identity authentication. In order to demonstrate the feasibility of the proposed multiple-image authentication method, a series of numerical simulations are performed, and the simulation results show that the proposed method exhibits high feasibility and security as well as authentication efficiency, and the metasurface for multiple-image authentication has strong robustness against cropping attack. • A metasurface-based multiple-image authentication method is proposed. • The proposed method has high information concealment and authentication efficiency. • Multiple identities of user holding the metasurface can be simultaneously verified. • The metasurface has strong robustness against cropping and noise attacks. [ABSTRACT FROM AUTHOR]

Tucker decomposition can provide an intuitive summary to understand brain function by decomposing multi-subject fMRI data into a core tensor and multiple factor matrices, and was mostly used to extract functional connectivity patterns across time/subjects using orthogonality constraints. However, these algorithms are unsuitable for extracting common spatial and temporal patterns across subjects due to distinct characteristics such as high-level noise. Motivated by a successful application of Tucker decomposition to image denoising and the intrinsic sparsity of spatial activations in fMRI, we propose a low-rank Tucker-2 model with spatial sparsity constraint to analyze multi-subject fMRI data. More precisely, we propose to impose a sparsity constraint on spatial maps by using an $ \ell _{p} $ norm (${0}< {p}\le {1}$), in addition to adding low-rank constraints on factor matrices via the Frobenius norm. We solve the constrained Tucker-2 model using alternating direction method of multipliers, and propose to update both sparsity and low-rank constrained spatial maps using half quadratic splitting. Moreover, we extract new spatial and temporal features in addition to subject-specific intensities from the core tensor, and use these features to classify multiple subjects. The results from both simulated and experimental fMRI data verify the improvement of the proposed method, compared with four related algorithms including robust Kronecker component analysis, Tucker decomposition with orthogonality constraints, canonical polyadic decomposition, and block term decomposition in extracting common spatial and temporal components across subjects. The spatial and temporal features extracted from the core tensor show promise for characterizing subjects within the same group of patients or healthy controls as well. [ABSTRACT FROM AUTHOR]

We study sparsity constrained nonlinear optimization (SCNO) from a topological point of view. Special focus will be on M-stationary points from Burdakov et al. (SIAM J Optim 26:397–425, 2016), also introduced as N C -stationary points in Pan et al. (J Oper Res Soc China 3:421–439, 2015). We introduce nondegenerate M-stationary points and define their M-index. We show that all M-stationary points are generically nondegenerate. In particular, the sparsity constraint is active at all local minimizers of a generic SCNO. Some relations to other stationarity concepts, such as S-stationarity, basic feasibility, and CW-minimality, are discussed in detail. By doing so, the issues of instability and degeneracy of points due to different stationarity concepts are highlighted. The concept of M-stationarity allows to adequately describe the global structure of SCNO along the lines of Morse theory. For that, we study topological changes of lower level sets while passing an M-stationary point. As novelty for SCNO, multiple cells of dimension equal to the M-index are needed to be attached. This intriguing fact is in strong contrast with other optimization problems considered before, where just one cell suffices. As a consequence, we derive a Morse relation for SCNO, which relates the numbers of local minimizers and M-stationary points of M-index equal to one. The appearance of such saddle points cannot be thus neglected from the perspective of global optimization. Due to the multiplicity phenomenon in cell-attachment, a saddle point may lead to more than two different local minimizers. We conclude that the relatively involved structure of saddle points is the source of well-known difficulty if solving SCNO to global optimality. [ABSTRACT FROM AUTHOR]

Least-squares reverse time migration (LSRTM) is powerful for imaging complex geological structures. Most researches are based on Born modeling operator with the assumption of small perturbation. However, studies have shown that LSRTM based on Kirchhoff approximation performs better; in particular, it generates a more explicit reflected subsurface and fits large offset data well. Moreover, minimizing the difference between predicted and observed data in a least-squares sense leads to an average solution with relatively low quality. This study applies L1-norm regularization to LSRTM (L1-LSRTM) based on Kirchhoff approximation to compensate for the shortcomings of conventional LSRTM, which obtains a better reflectivity image and gets the residual and resolution in balance. Several numerical examples demonstrate that our method can effectively mitigate the deficiencies of conventional LSRTM and provide a higher resolution image profile.

In recent years, the sparse system identification (SSI) has received increasing attention, and various sparsity-aware adaptive algorithms based on the minimum mean square error (MMSE) criterion have been developed, which are optimal under the assumption of Gaussian distributions. However, the Gaussian assumption does not always hold in real-world environments. The maximum correntropy criterion (MCC) is used to replace the MMSE criterion to suppress the heavy-tailed non-Gaussian noises. For some more complex non-Gaussian noises such as those from multimodal distributions, the minimum error entropy (MEE) criterion can outperform MCC although it is computationally somewhat more expensive. To improve the performance of SSI in non-Gaussian noises, in this brief we develop a class of sparsity-aware MEE algorithms with the fixed point iteration (MEE-FP) by incorporating the zero-attracting ($\ell _{1}$ -norm), reweighted zero-attracting (reweighted $\ell _{1}$ -norm) and correntropy induced metric (CIM) penalty terms into the cost function. The corresponding algorithms are termed as ZA-MEE-FP, RZA-MEE-FP, and CIM-MEE-FP, which can achieve better performance than the original MEE-FP algorithm and the MCC based sparsity-aware algorithms. Simulation results confirm the excellent performance of the new algorithms. [ABSTRACT FROM AUTHOR]

Hyperspectral unmixing refers to a source separation problem of decomposing a hyperspectral imagery (HSI) to estimate endmembers, and their corresponding abundances. Recently, matrix-vector nonnegative tensor factorization (MV-NTF) was proposed for unmixing to avoid structure information loss, which is caused by the HSI cube unfolding in nonnegative matrix factorization (NMF)-based methods. However, MV-NTF ignores local spatial information due to directly dealing with data as a whole, meanwhile, the forceful rank constraint in low-rank tensor decomposition loses some detailed structures. Unlike MV-NTF works at the original data, the pixel-based NMF is more adaptive to learn local spatial variations. Hence, from the perspective of multi-view, itis significant to utilize the complementary advantages of MV-NTF and NMF to fully preserve the intrinsic structure information, and exploit more detailed spatial information. In this article, we propose a sparsity-constrained coupled nonnegative matrix-tensor factorization (SCNMTF) model for unmixing, wherein MV-NTF and NMF are subtly coupled by sharing endmembers and abundances. Since the representations for abundances in MV-NTF and NMF are distinct, abundance sharing is achieved indirectly by introducing an auxiliary constraint. Furthermore, the L1/2 regularizer is adopted to promote the sparsity of abundances. A series of experiments on synthetic and real hyperspectral data demonstrate the effectiveness of the proposed SCNMTF method.

Abstract Background This study develops a model-based myocardial T1 mapping technique with sparsity constraints which employs a single-shot inversion-recovery (IR) radial fast low angle shot (FLASH) cardiovascular magnetic resonance (CMR) acquisition. The method should offer high resolution, accuracy, precision and reproducibility. Methods The proposed reconstruction estimates myocardial parameter maps directly from undersampled k-space which is continuously measured by IR radial FLASH with a 4 s breathhold and retrospectively sorted based on a cardiac trigger signal. Joint sparsity constraints are imposed on the parameter maps to further improve T1 precision. Validations involved studies of an experimental phantom and 8 healthy adult subjects. Results In comparison to an IR spin-echo reference method, phantom experiments with T1 values ranging from 300 to 1500 ms revealed good accuracy and precision at simulated heart rates between 40 and 100 bpm. In vivo T1 maps achieved better precision and qualitatively better preservation of image features for the proposed method than a real-time CMR approach followed by pixelwise fitting. Apart from good inter-observer reproducibility (0.6% of the mean), in vivo results confirmed good intra-subject reproducibility (1.05% of the mean for intra-scan and 1.17, 1.51% of the means for the two inter-scans, respectively) of the proposed method. Conclusion Model-based reconstructions with sparsity constraints allow for single-shot myocardial T1 maps with high spatial resolution, accuracy, precision and reproducibility within a 4 s breathhold. Clinical trials are warranted.

Digital pathology and microscopic image analysis play an important role in cell morphology research. In particular, the effective segmentation of White Blood Cells (WBCs) remains a challenging problem due to the blurring boundaries of WBCs under rapid staining, as well as the adhesion between leukocytes and other cells. In this paper, we propose a novel WBC (including nuclei and cells) segmentation algorithm based on both sparsity and geometry constraints. Specifically, we first construct a sparse image representation via combining the HSL color space and the RGB color channels, followed by the use of a sparsity constraint to only preserve useful information from the nuclei features. In addition, we introduce a robust model fitting strategy (i.e., the geometry constraint) to detect cells. Our model fitting strategy is able to significantly improve the robustness of the proposed segmentation algorithm against outliers that could seriously contaminate WBCs. The experimental results show that the proposed algorithm presents clear advantages over the state-of-the-art WBC segmentation algorithms in terms of accuracy.

This paper focuses on solving a challenging speech enhancement problem: improving the desired speech from a single-channel audio signal containing high-level unspecified noise (possibly environmental noise, music, other sounds, etc.). Using source separation technique, we investigate a solution combining nonnegative matrix factorization (NMF) with mixed group sparsity constraint that allows exploiting generic noise spectral model to guide the separation process. The experiment performed on a set of benchmarked audio signals with different types of real-world noise shows that the proposed algorithm yields better quantitative results in term of the signal-to-distortion ratio than the previously published algorithms.

Unsupervised feature selection is an indispensable pre-processing step in many data mining and pattern recognition tasks where the unlabeled high dimensional data are ubiquitous. Most of existing methods fail to explore the local geometric structure consistency (preservation) of the input data and minimize redundancy of selected features simultaneously. In this paper we propose a novel unsupervised feature selection method which jointly integrates the local geometric structure consistency and redundancy minimization (JLSPRM) into an unified framework. JLSPRM utilizes nonnegative spectral analysis to learn the cluster labels of the input data, then the local geometric structure consistency is developed to make the learned cluster labels more accurate, during which the feature selection operation is performed. To minimize the redundancy rate among selected features, the maximal information coefficient (MIC) is utilized to evaluate the correlation of the pairwise features. Besides, the ℓ2,1-norm is exerted on feature selection matrix which makes the framework decent for selecting features. An efficient iterative optimization algorithm is designed to obtain the solution of the unsupervised feature selection model. The superiority and effectiveness of our proposed approach over the state-of-the-art feature selection methods have also been validated through the extensive experiments on nine benchmark datasets. [ABSTRACT FROM AUTHOR]

In this paper, we study complexity results of sparse optimization problems and reverse convex optimization problems. These problems are very important subjects of optimization problems. We prove that the complexity result of the sparsity constraint problem and sparse solution problem are all NP-hard in the strong sense and even testing feasibility of the sparsity constraint is NP-complete in the strong sense. Then the sparse optimization problem is NP-hard in the strong sense. We also prove that the reverse convex problem is NP-hard in the strong sense by transforming the sparsity constraint into a reverse convex constraint. [ABSTRACT FROM AUTHOR]

In marine seismic exploration, the sea surface ghost causes frequency notches and low-frequency loss, which affects the signal-to-noise ratio (SNR) and resolution of seismic records. This paper presents a simultaneous receiver-side deghosting and denoising method based on the sparsity constraint. First, considering the influence of propagation direction and sea surface reflection coefficient, the ghost time delay is calculated accurately, and then the accurate ghost operator is constructed in the frequency—slowness domain. Finally, the ghost-free data are obtained using the sparse constraint algorithm that can effectively suppress the ghost along with the noise energy. This method can remove the ghost and noise simultaneously, achieving quick convergence and with few iterations. It is applied to synthetic data and actual streamer field data. Test results prove that the ghost and notches are suppressed effectively, the SNR is improved, and the band is well broadened. [ABSTRACT FROM AUTHOR]

In actual exploration, the demand for 3D seismic data collection is increasing, and the requirements for data are becoming higher and higher. Accordingly, the collection cost and data volume also increase. Aiming at this problem, we make use of the nature of data sparse expression, based on the theory of compressed sensing, to carry out the research on the efficient collection method of seismic data. It combines the collection of seismic data and the compression in data processing in practical work, breaking through the limitation of the traditional sampling frequency, and the sparse characteristics of the seismic signal are utilized to reconstruct the missing data. We focus on the key elements of the sampling matrix in the theory of compressed sensing, and study the methods of seismic data acquisition. According to the conditions that the compressed sensing sampling matrix needs to meet, we introduce a new random acquisition scheme, which introduces the widely used Low-density Parity-check (LDPC) sampling matrix in image processing into seismic exploration acquisition. Firstly, its properties are discussed and its conditions for satisfying the sampling matrix in compressed sensing are verified. Then the LDPC sampling method and the conventional data acquisition method are used to synthesize seismic data reconstruction experiments. The reconstruction results, signal-to-noise ratio and reconstruction error are compared to verify the seismic data based on sparse constraints. The LDPC sampling method improves the current seismic data reconstruction efficiency, reduces the exploration cost and the effectiveness and feasibility of the method. [ABSTRACT FROM AUTHOR]

In recent work [S. Soltani, M. Kilmer, and P. C. Hansen, BIT, 56 (2016)], an algorithm for nonnegative tensor patch dictionary learning in the context of X-ray CT imaging and based on a tensortensor product called the t-product [M. E. Kilmer and C. D. Martin, Linear Algebra Appl., 435 (2011), pp. 641--658] was presented. Building on that work, in this paper, we use nonnegative tensor patch--based dictionaries trained on other data, such as facial image data, for the purpose of either compression or image deblurring. We begin with an analysis in which we address issues such as suitability of the tensor-based approach relative to a matrix-based approach, dictionary size, and patch size to balance computational efficiency and qualitative representations. Next, we develop an algorithm that is capable of recovering nonnegative tensor coefficients given a nonnegative tensor dictionary. The algorithm is based on a variant of the modified residual norm steepest descent method. We show how to augment the algorithm to enforce sparsity in the tensor coefficients and note that the approach has broader applicability since it can be applied to the matrix case as well. We illustrate the surprising result that dictionaries trained on image data from one class can be successfully used to represent and compress image data from different classes and across different resolutions. Finally, we address the use of nonnegative tensor dictionaries in image deblurring. We show that tensor treatment of the deblurring problem coupled with nonnegative tensor patch dictionaries can give superior restorations as compared to standard treatment of the nonnegativity constrained deblurring problem. [ABSTRACT FROM AUTHOR]

A p‐norm extreme learning machine (ELM) based on sparsity constraint is presented in this study for tracking of fundamental frequency, harmonic and dc in current power signals which finds application in phasor measurement units for wide area power network in smart grid environment. Real‐time power applications typically are furnished with on‐board controller and hence have constraints to stock a complex architecture. Moreover, the data from online practices are polluted by noises of diverse statistical features obtained on a sample‐by‐sample basis. Hence, approaches with improved learning paradigm and close model dealing with noises of varied statistical characteristics are essential. The proposed approach formulates a cost function with recursive p‐norm error criterion and sparsity penalty that updates the output weights in succession besides adjusting some coefficients of the output weights to zeros that promotes quicker convergence and higher accuracy results. Exhaustive computer simulations have been carried out with synthetic signals and real‐time signals to track the dynamic changes in the power signal amplitude, phase and frequency that demonstrate the accuracy, efficiency and robustness of the proposed p‐norm ELM. Additionally, the new ELM network also is validated on a field programmable gate array (FPGA) hardware to prove its practicability towards current developments on phasor measurement units. [ABSTRACT FROM AUTHOR]

Full waveform inversion (FWI) is an extremely important velocity-model-building method. However, it involves a large amount of calculation, which hindsers its practical application. The multi-source technology can reduce the number of forward modeling shots during the inversion process, thereby improving the efficiency. However, it introduces cross-noise problems. In this paper, we propose a sparse constrained encoding multi-source FWI method based on K-SVD dictionary learning. The phase encoding technology is introduced to reduce crosstalk noise, whereas the K-SVD dictionary learning method is used to obtain the basis of the transformation according to the characteristics of the inversion results. The multi-scale inversion method is adopted to further enhance the stability of FWI. Finally, the synthetic subsag model and the Marmousi model are set to test the effectiveness of the newly proposed method. Analysis of the results suggest the following: (1) The new method can effectively reduce the computational complexity of FWI while ensuring inversion accuracy and stability; (2) The proposed method can be combined with the time-domain multi-scale FWI strategy flexibly to further avoid the local minimum and to improve the stability of inversion, which is of significant importance for the inversion of the complex model. [ABSTRACT FROM AUTHOR]

In this short communication, an algorithm for efficiently solving a sparse matrix equation, which arises frequently in the field of distributed control and estimation theory, is proposed. The efficient algorithm stems from the fact that the sparse equation at hand can be reduced to a system of linear equations. The proposed algorithm is shown to require significantly fewer floating point operations than the state-of-the-art solution. The proposed solution is applied to a real-life example, which models a wide range of industrial processes. The experimental results show that the solution put forward allows for a significant increase in efficiency in relation to the state-of-the-art solution. The significant increase in efficiency of the presented algorithm allows for a valuable widening of the applications of distributed estimation and control.

Multiple wave is one of the important factors affecting the signal-to-noise ratio of marine seismic data. The model-driven-method (MDM) can effectively predict and suppress water-related multiple waves, while the quality of the multiple wave contribution gathers (MCG) can affect the prediction accuracy of multiple waves. Based on the compressed sensing framework, this study used the sparse constraint under L0 norm to optimize MCG, which can not only reduce the false in the prediction and improve the image accuracy, but also saves computing time. At the same time, the MDM-type method for multiple wave suppression can be improved. The unified prediction of multiple types of water-related multiple waves weakens the dependence of conventional MDM on the adaptive subtraction process in suppressing water-related multiple waves, improves the stability of the method, and simultaneously, reduces the computational load. Finally, both theoretical model and practical data prove the effectiveness of the present method. [ABSTRACT FROM AUTHOR]

This paper investigates the generic signal shaping methods for the multiple-data-stream generalized spatial modulation (GenSM) and the generalized quadrature spatial modulation (GenQSM). Three cases with different channel state information at the transmitter (CSIT) are considered, including no CSIT, statistical CSIT, and perfect CSIT. A unified optimization problem is formulated to find the optimal transmit vector set under size, power, and sparsity constraints. We propose an optimization-based signal shaping (OBSS) approach by solving the formulated problem directly and a codebook-based signal shaping (CBSS) approach by finding the sub-optimal solutions in discrete space. In the OBSS approach, we reformulate the original problem to optimize the signal constellations used for each transmit antenna combination (TAC). Both the size and the entry of all signal constellations are optimized. Specifically, we suggest the use of a recursive design for the size optimization. The entry optimization is formulated as a non-convex large-scale quadratically constrained quadratic programming (QCQP) problem and can be solved by the existing optimization techniques with rather high complexity. To reduce the complexity, we propose the CBSS approach using a codebook generated by the quadrature amplitude modulation (QAM) symbols and a low-complexity selection algorithm to choose the optimal transmit vector set. The simulation results show that the OBSS approach exhibits the optimal performance in comparison with existing benchmarks. However, the OBSS approach is impractical for large-size signal shaping and adaptive signal shaping with instantaneous CSIT due to the demand of high computational complexity. As a low-complexity approach, the CBSS shows comparable performance and can be easily implemented in large-size systems. [ABSTRACT FROM AUTHOR]

Spectral unmixing (SU) is a technique to characterize mixed pixels in hyperspectral images measured by remote sensors. Most of the spectral unmixing algorithms are developed using the linear mixing models. To estimate endmembers and fractional abundance matrices in a blind problem, nonnegative matrix factorization (NMF) and its developments are widely used in the SU problem. One of the constraints which was added to NMF is sparsity, that was regularized by $ L_ {q}$ norm. In this paper, a new algorithm based on distributed optimization is suggested for spectral unmixing. In the proposed algorithm, a network including single-node clusters is employed. Each pixel in the hyperspectral images is considered as a node in this network. The sparsity-constrained distributed unmixing is optimized with diffusion least mean p-power (LMP) strategy, and then the update equations for fractional abundance and signature matrices are obtained. Afterward, the proposed algorithm is analyzed for different values of LMP power and $ L_ {q}$ norms. Simulation results based on defined performance metrics illustrate the advantage of the proposed algorithm in spectral unmixing of hyperspectral data compared with other methods. [ABSTRACT FROM AUTHOR]

The electrical capacitance tomography (ECT) is a visualization measurement method and can reconstruct the spatial permittivity distribution information in a measurement domain based on given capacitance values, in which the effectiveness of the image reconstruction algorithm plays a vital role in real-world engineering applications. Unlike common imaging methods, within the framework of the Tikhonov regularization methodology and the transform-domain sparsity method, a new cost function encapsulating the wavelet-based sparsity constraint is proposed to model the ECT imaging problem. An iteration scheme that integrates the superiorities of the alternating direction method of multipliers algorithm and splits a complicated optimization problem into several simpler sub-problems is developed to seek for the optimal solution of the proposed cost function. Numerical experiments validate that the proposed imaging algorithm is practicable and effective, and can improve the reconstruction accuracy and robustness. [ABSTRACT FROM AUTHOR]

Based on seismic array, the conventional frequency–wavenumber method, or the FK method, is generally used to determine the backazimuth and slowness parameters for the plane wave arriving at the seismic array. However, at low frequencies the FK method results in low-resolution estimation of both parameters. To overcome this issue, we have developed a new seismic array analysis method based on sparsity-constrained (SC) inversion to better determine the backazimuth and slowness parameters. The SC method takes advantage of the sparsity of the incoming wave front in the domain of slowness and backazimuth. We have tested the proposed SC method using synthetic data calculated for Shanghai Earthquake Agency Array (SEAA) from one single source and two sources, respectively. Compared to the FK method, the proposed SC method has a much higher resolution in estimating the backazimuth and slowness parameters. Furthermore, the SC method can more easily separate multiple sources and estimate the two parameters. We also compare the proposed SC method with another advanced seismic array analysis method CLEAN-PSF, which can find the position and strength of point sources. Overall, our proposed SC method performs better than or at least at the comparable level as the CLEAN-PSF method. We further demonstrate the effectiveness of the new method on the 2008 M w 8.0 Wenchuan earthquake data recorded on the SEAA. The deviation between theoretic backazimuth and optimal solution is approximately 4°, indicating the capability of the proposed SC method for reliably estimating the backazimuth of teleseismic event based on a seismic array. [ABSTRACT FROM AUTHOR]